By intensive monitoring of AGN variability over a large range in wavelength, we can probe the structure and physics of active galactic nuclei on microarcsecond angular scales. For example, multi-wavelength variability data allow us (a) to establish causal relationships between variations in different wavebands, and thus determine which physical processes are primary and which spectral changes are induced by variations at other wavelengths, and (b) through reverberation mapping of the UV/optical emission lines, to determine the structure and kinematics of the line-emitting region, and thus accurately determine the central masses in AGNs. Multiwavelength monitoring is resource-intensive, and is difficult to implement with general-purpose facilities. As a result, virtually all programs undertaken to date have been either sparsely sampled, or short in duration, or both. The potentially high return on this type of investigation, however, argues for dedicated facilities for multiwavelength monitoring programs.